Manufacturing processes such as fabrication of semiconductor wafers use the basic technique of positioning objects to be processed or to be inspected. Hypothesis testing fitting has been used to estimate a parameter associated with, for example, the position of an object such as the center of the object shape with high accuracy.
For example, Patent Literature 1 below describes a hypothesis testing fitting technique for calculating the central position of a wafer based on the outline of the wafer. This technique prevents the central position of the wafer from being calculated erroneously by erroneously detecting the position of the outline of the wafer.
With this technique, the coordinates of at least four points on the wafer outline are detected (at least four detection points are obtained), and all combinations of three points (three selection points) are determined from the coordinate values of the plurality of detected points on the outline (or edge), and the coordinates of the central position (the central position as the calculated value) are calculated for each combination of three points. The variation in the calculated coordinates of the central positions is then calculated. When the variation does not exceed a predetermined threshold, the edge detection is determined successful. This technique prevents the central position of a wafer from being calculated erroneously by erroneous detection through image processing.